Next time you get a chance, pop into your local jewelry store and take a look at the gems. Notice anything about them? They're all tiny, on the order of the size of a pinhead. If you pried every stone in the place loose from its setting and piled them up, the entire heap would probably fit in a soup pot. (And then you would be arrested, but that's beside the point.)

In Real Life, gem-quality stones larger than a person's fingernail are so rare that they are almost never for sale on the open market. This doesn't apply in fiction, where a single gem can easily be the size of your fist... head... torso... you get the idea. It's also not very uncommon if gems that are mined are already cut.

When it comes to gold, the problem is not size (unless you're talking City of Gold quantities) but weight. Most of us only ever see gold in tiny quantities (and usually alloyed with lighter metals) so it's hard to notice that it's more than twice the density of lead. A standard gold bar weighs about thirty pounds, so if the guys pulling off The Caper are carrying more than one or two at a time, they're not going to be hard to catch.

In Video Games, it gets even more ridiculous. Not only are gemstones enormous, but the same thing largely applies to money or even pieces of jewelry, especially in platform games. In video games, this is also often done for convenience because finding coins, jewelry or rings as small as a thumbnail can be rather hard since that would often mean that they would take up a space of a size less than a pixel. (Compare Units Not to Scale.) Of course, characters themselves have enough hammerspace to fit a lot of them in their pockets.

Additionally there is often some Artistic License – Geology (or possibly Everything's Better with Sparkles) in cartoons referencing valuable minerals, particularly diamonds. In fiction you'll often see a mineral faceted, polished, and/or sparkling straight out of the ground. In Real Life, clean and perfectly formed crystals are rare in nature, and most rough gems (at least to the inexpert eye) just look like dirty pebbles. We call this All-Natural Gem Polish, a closely related trope.

Examples of works with huge gemstones:

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Comic Books

In The Maniaks, Silver Shannon was given an engagement ring containing a diamond bigger than her head.

Film

The Mummy Returns has a pyramid topped with an approximately man-sized diamond. At the end, Jonathan grabs it while suspended from a dirigible, though its weight should realistically be enough to dislocate his shoulders were he to try such a thing.

The diamond in Snatch. has a diameter of about 4-5 centimetres (1.6 inches) and weighs 86 carats. Notably, everyone in the film who knows anything about jewelry makes a huge deal about its size.

Alfred mentions "a ruby the size of a tangerine" as one of the precious stones the bandit he fought in That South East Asian Country had stolen and given away. We never actually see it though so it's entirely possible he was exaggerating.

Literature

Invoked in-universe in Moving Pictures, in which the faux-tunnel used to film the mining scene in Blown Away had cut-glass gemstones the size of chickens set into its walls.

Also in the Discworld, in Reaper Man, where Death gives an 800 carat diamond called the Tear of Offler (a crocodile god) as a gift to Renata Flitworth.

In The Worm Ouroboros by E R Eddison we have this in the description of the king's palace:

But the great wonder of this chamber, and a marvel to behold, was how the capital of every one of the four-and-twenty pillars was hewn from a single precious stone [...] all hewn from faultless gems, thrice the bulk of a big man's body

In Dragon Queen, the Dragon Queen in the old man's story tried to steal a large statue made of gold.

"The Diamond As Big As the Ritz" from a short story of the same name by F. Scott Fitzgerald, it is supposed to be one of the mountain-sized variety.

Artemis Fowl has Artemis extort one ton of gold from the fairies. However, its weight is irrelevent as it's brought in on a hover trolley.

Live-Action TV

In the Stargate SG-1 episode "Ascension", Orlin makes a large emerald for Major Carter, destroying her microwave in the process. When Carter remarks about how large the gem is, Orlin claimed it was difficult to figure out the gem's typical size from a book.

Averted in Castle Season 6, Episode 8, "A Murder Is Forever", in which the group finds a diamond about as big as a man's palm, and spend a big chunk of the rest of the episode trying to find out how such an absurdly large diamond could exist without the entire world knowing. It turns out to be the prototype of a breakthrough technique that can synthesize flawless diamonds of any size, rendering diamond mines superfluous.

Done semi-reasonably in an episode of Mission: Impossible where the team is sent to steal the world's largest diamond from a dictator. The diamond weighs about eight pounds uncut and is about the size of a shoe. Large, but not ridiculously so, and the stone is explicitly stated to be one of a kind.

Video Games

Since Rupees in The Legend of Zelda are specifically used as currency in Hyrule, scroll down to the Huge Currency section for details.

The Sonic the Hedgehog series has the Chaos Emeralds, seven fist-sized gems of varying colors, and the Master Emerald, a gemstone the size of a full-grown man. In addition to being implausibly large, they also give you super-powers, which real emeralds seldom do.

One of the maps in City of Heroes is a cave with enormous gemstones in the walls, easily as big as your character. Presumably these gemstones are so common that they're not worth mining, especially given the danger of being nobbled by supervillains while down there.

In Crystal Caves the eponymous crystals are the size of your protagonist.

The Legend of Kyrandia has the Kyragem, a powerful magical artifact. It is roughly as wide as a regular kitchen table and set into the ground. May not count since not only is it a powerful magical artifact, it's the powerful magical artifact that's the source of all the magic in the kingdom.

In World of Warcraft, everything tends to have exaggerated proportions for stylistic reasons, so all gemstones follow this trope, but the most extreme example is Oshu'gun, a mountain-sized diamond that was originally a sort of magical dimension-traveling spaceship.

The Elder Scrolls V: Skyrim at least tries to avert this as much as what would be practical. All of the gemstones you find in the game are larger than your thumb, but if you drop one, finding it again easily risks becoming a Pixel Hunt.

However, gathering a large number (probably around 10-20 or so) into your inventory then dropping the whole lot of them all at once sometimes resulted in one gigantic gem the size of a dagger.

Averted in Grand Theft Auto IV. A bag of diamonds becomes a recurring plot point, but even though one scene has a character talk about how high quality they are, the gems themselves are fairly small.

Averted in Baldurs Gate Dark Alliance where the gems used to enchant items and weapons are so tiny, the player can't even see what they are until picked up (as the camera is in the typical Diablo hack-n-slash angle). This would normally be very annoying, but fortunately gems sparkle when dropped, and you only need to be near an item to be given the pick-up prompt.

Pearls in Beyond Good & Evil tend to be approximately the size of the main character's head.

Paul (narrating): Sitting before me was the largest sapphire I had ever seen. It was uncut, a slightly dull blue in appearance, a lumpy, amorphous blue rock, but I'd seen enough gems to know what it was I was looking at. Now, in case you're not familiar with jewels, and think that "a big gemstone" is like something out of a cartoon, large enough to sit on like a stool, allow me to disabuse you of the notion. This rough sapphire was about half the size of a chicken's egg, and that's freaking enormous as gems go!

Later on in the story, it also gets gold right: Paul recognizes that a golden statuette of a warrior, about two feet tall, would probably weigh about as much as he does, if not more, and he'd have trouble lifting it without help.

Western Animation

DuckTales - Constantly, but taken to extremes in the Ali Bubba's Cave trilogy which revolves around a massive diamond mine, all featuring All-Natural Gem Polish of course, with the final episode featuring an enormous diamond easily the size of a minivan.

You should see the NES game, where every treasure (all worth $1 million) at the end of every level is huge, even giant coins.

The original film that began The Pink Panther franchise also features a gem of considerable size and weight.

In The Rescuers, Madame Medusa uses Penny to get the Devil's Eye, supposedly the biggest diamond in existence.

In the Futurama episode "Where the Buggalo Roam", the native Martians sold their land for what they thought was a glass bead, with which they plan to crush Kif. It turns out to be a gigantic diamond. After the protagonists explain how much it's worth, the Martians decide they don't need their land back.

"This planet's a dump anyway. We'll buy a NEW planet and CALL it holy. With cash like this, who's gonna argue? No one, that's who."

One episode of Jimmy Neutron has Jimmy and friends making use of boulder-sized, polished, and cut diamonds they found sticking out of a mountain face...

In My Little Pony: Friendship Is Magic, all the gems and jewels are... quite big. And numerous enough that Rarity can make just about anything she wants Gem-Encrusted, which is her design trick of choice. Spike can also eat them by the bowlful without anyone getting mad.

"Hearth's Warming Eve" reveals that when Equestria was first settled in, gems the size of ponies were jutting out of cliff faces everywhere.

Balancing out the size and commonality of gems is their low value. A (human) fist-sized dazzling cut gemstone is considered a generous tip for a bellhop, treated like giving one IRL a twenty dollar bill.

Looney Tunes short "Ali Baba Bunny" had a treasure room chock full of huge gems-Daffy Duck tries to abscond with one as big as he was. Later, he tries to take a pearl of the same scale but he had been shrunk by then, so it was actually a normal-sized one.

The biggest diamonds in the universe are located in the white dwarf stars with carbon cores. Technically they're enormous single diamonds, but good luck mining them...

Also, it's unlikely that they actually look like jewels, despite of having diamond composition - most of the diamonds used in diamond-edged blades, among other things, look rather like gray dust to a bare eye.

Additionally, there's the planet PSR J1719-1438 b, which probably is a diamond the size of Jupiter.

Carbon-rich planets in general would likely contain thick layers of underground diamond due to the heating and compression of their carbon crusts. If tectonic pressures subsequently lifted these layers above the surface, such planets could potentially have mountains of diamond. However, as noted these would not look shiny.

The world's largest gold coin is the size of a large pizza. And the weight of a large man.

And the world's largest copper coin is a big copper plate weighing about 40 pounds.

The largest rough gem-quality diamond ever discovered, the Cullinan, was about four inches long and weighed over a pound (3106.75 carats before cutting). After cutting, the largest stone of the Cullinan, the Great Star of Africa was 530.4 carats. The Koh-i-Noor, literally "Mountain of Light," was once the largest known, but as it was first cut thousands of years ago in India nobody is sure how big it originally was, and the British Crown had it recut down to only 105.6 carats. Both reside in the UK Crown Jewels today. The largest cut diamond today is the Golden Jubilee, at 545 carats, though the Golden Jubilee was smaller than the Cullinan in the rough, its shape was better for cutting into a single large stone.

Diamonds are small fry compared to some other stones. The largest piece of Jade resides in Myanmar, uncut in its natural state. It weighs over 30 tons.

The largest pearl, the Pearl of Lao Tzu, weighs over 14 pounds.

One of the larger cut gems is the Dom Pedro Aquamarine. The uncut crystal weighed over 100 pounds and was three feet long. The finished piece is 14 inches long and weighs 10,363 carats. It resides in the Smithsonian in Washington DC.

The American Golden Topaz is possibly the largest faceted stone in the world, at 22,500 carats. It's about the size of a human head, making it nearly as big as many fictional stones.

The Millenium Sapphire is an opaque sapphire carved into a statue of a caravan. It weighs 61,500 carats in total.

Synthetic sapphire is made in lumps up to half a ton in weight. Now, they are normally uncolored (technically, corundum) and mainly used to make windows, but it's theoretically quite possible to make a million-carat gem.

Examples of works with huge money and jewelry:

Newspaper Comics

One Garfield comic had him singing on the fence for a Boy Scout troop from a made-up island. After one of the scouts throws a boot at him, Garfield angrily tells them to at least throw money if they must throw something at him. Next panel has him being knocked over by a large object and commenting that he forgot that the only currency on that island was "forty-pound chariot wheels".

Not exactly a newspaper comic, but a serial called "Wormy" that was featured in Dragon Magazine used this trope. Seen here, When Jed enters a pub to buy a drink.

Literature

In The Restaurant at the End of the Universe, the exchange rate of eight Ningis to one Pu "is simple enough, but since a Ningi is a triangular rubber coin 6,800 miles along each side, no-one has ever collected enough to own one Pu."

One of the stories in Pavel Bazhov's Malachite Casket, a collection of fairy tales based on the Ural miners' folklore, has a guy to make a bet with a mountain spirit (in form of a girl) to receive a treasure if he guesses the right one. A first treasure is a large tray heaped with gold nuggets, that he (being a miner and gold prospector) correctly assumes to weigh almost a ton that no girl can hold so effortlessly. The second is a basket of jewels the also unrealistically sized from the human fist to a football.

Tabletop Games

The largest unit of the Jade currency of the Realm in Exalted is a slab referred to as a talent, which is 24x48 inches and weighs almost seventy pounds. Even its lesser denominations, the bar and the mina, weigh more than a pound and are several inches long. The impracticalities of their size (and their very high value) means that such units are rarely used in actual transactions or even owned in their whole forms; they're more often just moneys of account.

Video Games

The Super Mario Bros. series has coins as tall as small Mario. Lots of games also feature special coins, such as those with Yoshi's likeness, which are larger than even large Mario.

The Legend of Zelda, naturally. Rupees are as large as Link's sprite in the original game, as well as several handheld games. Recent games have most rupees represented as slightly smaller, although the large-denomination rupees still closely match Adult!Link for size.

Link also holds everything up, and it's exactly the size of Link's sprite.

Bell bags in Animal Crossing series are drawn much larger than would fit in the character's pocket.

Banana coins, bear coins, and the like in Donkey Kong Country series. There are even very large coins in Donkey Kong 64... which you don't pick up; they're for standing on.

Serious Sam II had coin pickups which give points when picked up and like any decent item in the game, constantly spinning mid-air.

Real Life

Surprisingly, this has been Truth in Television at least once. The rai of Yap Island were stone wheels with holes; the largest one discovered measured 4 meters in diameter. These are still used today in ceremonial purposes. Sometimes the inhabitants agree that a stone has changed hands, and leave it where it lies. One of them is legal tender despite lying at the bottom of the ocean. Much like our cash can be exchanged despite lying in a distant vault.

This planet's a dump anyway. We'll buy a NEW planet and CALL it holy. With cash like this, who's gonna argue? No one, that's who.

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